A penalized version of the local minimization scheme for rate-independent systems. (May 2021) - Knees, Dorothee; Shcherbakov, Viktor
Abstract: The letter presents a penalized version of the time-discretization local minimization scheme first proposed by Efendiev and Mielke in 2006 to resolve time discontinuities in rate-independent systems with nonconvex energies. In order to penalize inequality constrains enforcing the local minimality, the Moreau–Yosida approximation is employed. We prove the convergence of time-discrete solutions to functions that are parametrized BV solutions of the time-continuous problem (in an abstract infinite-dimensional setting), provided that the discretization and approximation parameters are chosen appropriately. We test our scheme on a one-dimensional example and find a notable improvement compared with the original version.